An Adaptive Domain Partitioning Technique for Meshfree-Type Methods

الملخص EN

An overlapping domain partitioning based on adapting nodes is presented for the meshless-type methods.

The decomposition of the domain is carried out based on the distribution of the nodes produced rather than the geometry of the problem.

A set of adaptive nodes is first generated using the dimension reduction and equidistributing along the coordinate directions with respect to arc-length monitor.

The domain is then partitioned in such a way that the same number of nodes are allocated to the subdomains.

A radial basis function collocation method is applied to each subdomain followed by assembling the global solution from the subproblem's solutions.

A generalized thin plate spline with sufficient smoothness is used as a basis function in the collocation method.

Some numerical results will be presented to show the performance of the proposed method.